What is the importance of low poly vs high poly?
Highpoly is important to achieve superb surface detail. The problem is how you control such enormous amount of vertices:


with brushes (sculpting)
through control low-poly cages (subdivision surfaces)
through curve or nurbs surfaces
generated by some simulation, 3D scanning, etc.


Lowpoly is important for:


game-engines
subdivision modelling
low-polygon proxy geometries of high-poly ones - for rigging and animating
low-poly style and such..


Problem with low-poly is topology, which has to follow some rules, so the shading looks righ, the subdivision surfaces are right or the sculpts will be right. That's why you see so much about low-poly - with knowledge about low-poly topology the high-poly comes along.


You convert low-poly to high-poly through sculpting, or catmull-clark subdivision
You convert high-poly to low-poly through retopology, or decimation. The details from high-poly can be baked into texture maps.


What is considered low-poly and high-poly changes with time and computer power, it's safe to say that low-poly is everything that can be displayed on target hardware in real-time. That means that for mobile phone this is different than for workstation.

Appropriate level of detail depends on how small the object will be on screen - basically how much pixels it will cover on screen:


for textures on lowpoly you want them 2x larger than a texture that has same size pixels on a model as a pixels on screen. This is because texture filtering. Or how the target hardware GPU memory lets you use.

For game models this is usually from 1024x1024 to 4096x4096 or more for next-gen.
For mobile-phones aroung 256x256 to 512x512.

for lowpoly polycounts:

around 10k for character or more for next-gen. Depends on the object size, hardware, if it is in background or not etc. 

for highpoly you want the polygons small enough that the surface detail will be well defined, this is usually smaller than screen pixel size or even smaller than that. Polycounts in millions.